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Multivariate Stochastic Volatility with Cross Leverage

Author

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  • Tsunehiro Ishihara

    (Graduate School of Economics, University of Tokyo)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

Abstract

We describe and estimate for the first time a natural multivariate extension of the univariate stochastic volatility model with leverage. The model, which we call the multivariate stochastic volatility with cross leverage, is fit by a tuned Bayesian MCMC method. Of particular general interest is our approach for sampling the state variables from the posterior distribution conditioned on the parameters. The state variables are sampled in blocks by the Metropolis-Hastings algorithm in which the proposal density is derived from an approximating linear Gaussian state space model. The conditional modes of the latent volatility variables are computed using a method of scoring where the covariance matrix of the proposal density is guaranteed to be positive definite. The auxiliary particle filter to compute the likelihood function is also shown and the model and the techniques are illustrated with daily stock returns data from the Tokyo Stock Exchange.

Suggested Citation

  • Tsunehiro Ishihara & Yasuhiro Omori, 2009. "Multivariate Stochastic Volatility with Cross Leverage," CARF F-Series CARF-F-191, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  • Handle: RePEc:cfi:fseres:cf191
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    Cited by:

    1. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," "Marco Fanno" Working Papers 0124, Dipartimento di Scienze Economiche "Marco Fanno".
    2. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, Elsevier.
    3. Geert Mesters & Bernd Schwaab & Siem Jan Koopman, 2014. "A Dynamic Yield Curve Model with Stochastic Volatility and Non-Gaussian Interactions: An Empirical Study of Non-standard Monetary Policy in the Euro Area," Tinbergen Institute Discussion Papers 14-071/III, Tinbergen Institute.
    4. Kurose, Yuta & Omori, Yasuhiro, 2016. "Dynamic equicorrelation stochastic volatility," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 795-813.
    5. Caporin, Massimiliano, 2013. "Equity and CDS sector indices: Dynamic models and risk hedging," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 261-275.
    6. Ishihara, Tsunehiro & Omori, Yasuhiro, 2012. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3674-3689.
    7. Caporin, Massimiliano & McAleer, Michael, 2014. "Robust ranking of multivariate GARCH models by problem dimension," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 172-185.
    8. Asai, Manabu & Caporin, Massimiliano & McAleer, Michael, 2015. "Forecasting Value-at-Risk using block structure multivariate stochastic volatility models," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 40-50.
    9. Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 331-350.
    10. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    11. Diks, Cees & Panchenko, Valentyn & Sokolinskiy, Oleg & van Dijk, Dick, 2014. "Comparing the accuracy of multivariate density forecasts in selected regions of the copula support," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 79-94.
    12. Skaug, Hans J. & Yu, Jun, 2014. "A flexible and automated likelihood based framework for inference in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 642-654.
    13. Caldeira, João F & Moura, Guilherme Valle & Santos, André Alves Portela, 2013. "Seleção de carteiras utilizando o modelo Fama-French-Carhart," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 67(1), April.
    14. repec:fgv:epgrbe:v:67:n:1:a:3 is not listed on IDEAS
    15. João Caldeira & Guilherme Moura & André Santos, 2015. "Measuring Risk in Fixed Income Portfolios using Yield Curve Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 65-82, June.
    16. Trojan, Sebastian, 2014. "Multivariate Stochastic Volatility with Dynamic Cross Leverage," Economics Working Paper Series 1424, University of St. Gallen, School of Economics and Political Science.
    17. Santos, André A.P. & Moura, Guilherme V., 2014. "Dynamic factor multivariate GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 606-617.
    18. Sujay K Mukhoti, "undated". "Dynamic Feedback Effect And Skewness In Non-Stationary Stochastic Volatility Model With Leverage," Working papers 145, Indian Institute of Management Kozhikode.

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